Nonlinear non-minimum phase output tracking via output redefinition and learning control

Controllers are developed to achieve precise tracking control of single-input single-output nonlinear non-minimum phase systems affine in the control input. In addition to being non-minimum phase, the nonlinear systems considered are assumed to not be precisely characterized (i.e., there are uncertainties present). The control objective is to have the output of such systems track periodic reference trajectories. The developed controllers make novel use of: feedback linearization, output redefinition, and repetitive learning control. Output redefinition is employed in the following way: (1) a new output is defined such that the resulting new system is minimum phase, and (2) a desired redefined output trajectory is computed for the redefined output to track, such that in the process the original output precisely tracks the original desired output trajectory. A suitable redefined output is determined based on an approximate feedback linearization method. The redefined output obtained in this way results in a locally input-output linearized system with no zero dynamics. A control input obtained from feedback linearization based on this redefined output is then directly applied to the nonlinear system. The desired redefined output trajectory is calculated on-line as the output of new repetitive learning controllers that are developed and analyzed. The input to each learning controller is the original output tracking error. Simulations, and experiments performed on an underactuated mechanical system characterized by uncertainties, demonstrate the effectiveness of the developed controllers.